Controllability of Kinematic Control Systems on
نویسندگان
چکیده
Many interesting and important control systems evolve on strati ed con guration spaces. Robotic systems, in particular, are of this nature. A legged robot has discontinuous equations of motion near points in the con guration space where each of its \feet" come into contact with the ground, and it is precisely the ability of the robot to lift its feet o of the ground that enables it to move about. Similarly, a robotic hand grasping an object often cannot reorient the object without lifting its ngers o of the object. Despite the obvious utility of such systems, however, a comprehensive means to analyze their controllability properties, to our knowledge, has not appeared in the literature. For such systems, the equations of motion on each strata may change in a non{smooth, or even discontinuous manner, when the system moves from one strata to another. In such cases, traditional nonlinear controllability analyses are inapplicable because they rely upon di erentiation in one form or another. Yet it is the discontinuous nature of such systems that is often their most important characteristic. Therefore, it is necessary to incorporate explicitly into a controllability analysis the non{smooth or discontinuous nature of these systems. We present two controllability tests for strati ed, kinematic control systems. We assume that the con guration manifold for the control system contains submanifolds with codimension one, in which the system is subjected to constraints in addition to those present outside the submanifold. Submanifolds of higher codimension may be de ned by the intersection of two lower codimension submanifolds. To use the rst test, we consider the geometric relationship among involutive distributions associated with the various (sub)manifolds at a point in the conguration manifold. We note that the involutive distribution associated with a particular submanifold is more than simply the involutive closure of the control
منابع مشابه
Controllable kinematic reductions for mechanical systems: concepts, computational tools, and examples
This paper introduces the novel notion of kinematic reductions for mechanical systems and studies their controllability properties. We focus on the class of simple mechanical control systems with constraints and model them as a ne connection control systems. For these systems, a kinematic reduction is a driftless control system whose controlled trajectories are also solutions to the full dynami...
متن کاملON CONTROLLABILITY AND OBSERVABILITY OF FUZZY CONTROL SYSTEMS
In order to more effectively cope with the real world problems of vagueness, imprecise and subjectivity, fuzzy event systems were proposed recently. In this paper, we investigate the controllability and the observability property of two systems that one of them has fuzzy variables and the other one has fuzzy coefficients and fuzzy variables (fully fuzzy system). Also, sufficient conditions for ...
متن کاملLow-Order Controllability and Kinematic Reductions for Affine Connection Control Systems
Controllability and kinematic modelling notions are investigated for a class of mechanical control systems. First, low-order controllability results are given for the class of mechanical control systems. Second, a precise connection is made between those mechanical systems which are dynamic (i.e., have forces as inputs) and those which are kinematic (i.e., have velocities as inputs). Interestin...
متن کاملControllability of kinematic control systems on stratified configuration spaces
This paper considers nonlinear kinematic controllability of a class of systems called stratified. Roughly speaking, such stratified systems have a configuration space which can be decomposed into submanifolds upon which the system has a different set of equations of motion. For such systems, then, considering controllability is difficult because of the discontinuous form of the equations of mot...
متن کاملStructural Properties of Multirate Sampled-Data Systems
The application of Networked Control Systems (NCS) in which sensory and control signals are transmitted via shared data communication networks, is growing significantly and these systems have been the subject of research during the last decade. On the other hand, multirate sampled data systems have been investigated since a long time. In this paper, conditions under which a networked control sy...
متن کامل